Emboss or deboss a more complex logo into a mesh
Here's a quick guide for doing it with microdisplacement. Note this won't work for you if you actually need a good mesh, but it'll give a result similar to your reference image.

1) Enable Blender's experimental feature set:



2) Add a new Cycles materal, and set its displacement method to True:



3) Add a subsurf modifier; select Simple, and enable adaptive rendering:



4) From edit mode, select all vertices and unwrap the plane (U):



5) In an image editor, threshold your logo and blur it a bit:



6) Add the image texture to the displacement at your material output node:



The result should look something like this: